In recent years, as demands for higher gain to error-correcting codes to be applied to communication systems have increased, higher-gain codes of a type of performing iterative decoding using soft-decision codes such as turbo (convolution) code, LDPC code, and turbo product code are increasingly used. Further, as the quantity of communications increases regardless of transmission systems such as wireless/wired communication systems or storage systems such as recording mediums, demands for larger-capacity communication systems have also increased.
Input signals of a decoder used for such high-gain codes are signals called LLR. Originally, an LLR of a quadrature modulation (quadrature amplitude modulation: QAM) in which signal point is arranged two-dimensionally is calculated based on a square distance of the reception signal points expressed in two dimensions and all signal points (16 pieces if 16 QAM). Since the square distance calculation is complicated, there has been used a method generally in which a table computed and generated beforehand by a program is stored in a ROM (Read Only Memory) or in a logic circuit (truth table) corresponding to a ROM, and an LLR is calculated with reference to the stored table (see, for example, Non-Patent Document 1).
Further, as an apparatus of calculating an LLR by arithmetic operation, Patent Document 1 discloses an apparatus which calculates a log likelihood ratio of each bit in an M-ary OAM modulated signals to be transmitted in a communication system efficiently in order to reduce the time arithmetic time of LLR.
Patent Document 1: Japanese Patent Laid-Open Publication No. 2002-330188    Non-Patent Document 1: “AHA Application Note Non-Square QAM Implementation for AHA 4540”, AHA Inc.